

A226665


Conjectured recordbreaking maximal values, for ascending positive integers k, of the minimal elements of the primitive cycles of positive integers under iteration by the Collatzlike 3x+k function.


2



1, 347, 7055, 177337, 212665, 219913, 379541, 413803, 822535, 1391321, 8013899, 21619279, 21834347, 28306063, 37550317, 168536521, 189763177
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

A cycle is called primitive if its elements are not a common multiple of the elements of another cycle.
The 3x+k function T_k is defined by T_k(x) = x/2 if x is even, (3x+k)/2 if x is odd, where k is odd.
For primitive cycles, GCD(k,6)=1.


LINKS

Table of n, a(n) for n=1..17.


EXAMPLE

a(1)=1 because {1,2}, with minimal element 1, is the only known '3x+1' cycle of positive integers.
k=5 is the next value of k>1 with GCD(k,6)=1. The minimal element in each of the five known primitive '3x+5' cycles of positive integers is 1, 19, 23, 187 and 347. 347>a(1) so a(2)=347.


CROSSREFS

k = A226666(n).
Cf. A226607, A226681.
Sequence in context: A190814 A012868 A226669 * A185713 A264384 A323999
Adjacent sequences: A226662 A226663 A226664 * A226666 A226667 A226668


KEYWORD

nonn


AUTHOR

Geoffrey H. Morley, Jun 16 2013


STATUS

approved



